Let A=(acbd),abcd=0 A2=(acbd)⋅(acbd)⇒A2=(a2+bcac+cdab+bdbc+d2)⇒a2+bc=1,bc+d2=1ab+bd=ac+cd=0c=0 and b=0 Trace A=a+d=0∣A∣=ad−bc=−a2−bc=−1.
Let A be a 2×2 matrix with non-zero entries and let A2=1, where 1 is 2×2 identity matrix. Define Tr(A)= sum of diagonal elements of A and ∣A∣= determinant of matrix A. Statement-1: Tr(A)=0 Statement-2: ∣A∣=1
Held on 30 Apr 2010 · Verified 6 Jul 2026.
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1
Statement-1 is true, Statement-2 is false
Statement-1 is false, Statement-2 is true
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1
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